Yvette Cooper, the shadow work and pensions secretary, today rounded on the coalition government for launching the "biggest assault on the family in the entire history of the welfare state" as she urged the party to fight cuts that "pick on the weakest".

Cooper, one of the party's most high-profile female politicians who is tipped to top Labour's upcoming shadow cabinet elections, told delegates that George Osborne, the chancellor, has chosen to set out old-fashioned Tory cuts that hit the poorest hardest instead of outlining welfare reforms that got people back into work.

She accused Osborne of "swaggering round like the playground bully – working out who won't fight back, picking on the weakest – and that's just Iain Duncan Smith", referring to the work and pensions secretary, who is locked in dispute with the chancellor over welfare reform.

"Hitting the poorest harder than the rich, women harder than men; hitting the sick and disabled; pensioners and children are being hit hardest of all."

Seizing on Tory minister Theresa May's infamous description of the Conservatives as "the nasty party", Cooper said the coalition's emergency budget and its planned spending cuts meant the "nasty party is back, and this time they've brought their mates".

Osborne's budget would hit women three times as hard as men, even though they earned and owned less than men, she said.

Citing the low number of women now in government, Cooper said the coalition cuts showed they failed to understand women's lives, claiming that of the £8bn raised from the chancellor's budget, £6bn of it was from spending affecting women.

"Nick Clegg says things like working tax credits, child benefit, carers' allowance make people dependent and should be cut back," said Cooper. "For millions of women across Britain the opposite is true. The tax credits help mums pay for childcare so they can go out to work. The carers' allowance helps daughters look after their elderly parents.

"That support doesn't make them dependent. It gives them greater independence, greater choice about how to cope with the different pressures of work and family life."

She told delegates she had always assumed that each generation of women would do better than the last, but now she found herself worrying about the future for her two young daughters.

"I know I've had more choices, more opportunities than my mother and my grandmother, not least because of the battles they won. With each generation, I assumed, we would break more glass ceilings, change more of the world.

"But now, for the first time, I worry about my daughters, about all our daughters. For the first time I worry that our daughters will have fewer chances in life than we did. Conference, for women across Britain, backed by the Labour party, the fightback starts here."

Cooper is seen as a possible future shadow chancellor – as is her husband, Ed Balls, who used the Labour leadership race to argue against the coalition's drastic cuts as damaging to the economy.

Today Cooper said cutting the deficit far too fast would cause "deep damage" to women, children, the elderly and young people looking to get into work.

"Of course the deficit does need to come back down, and that will mean tough and unpopular decisions. But cutting jobs to get the deficit down? What planet are they on?"

Cooper hailed the former Labour government's record on job creation and tackling the economic crisis, but she conceded that the party should have started sooner on reforms to help people off long-term sickness benefits and into work.

Labour should also go further in forcing people to take up jobs: "Opportunities alongside obligations."

But she rounded on the government for claiming to help more people into work while planning to cut jobs for them to go into.

Cooper attacked the prime minister, David Cameron, for scrapping the Future Jobs Fund, which he had previously said was a good scheme, and urged the party to ensure every conceit and deceit of the government was exposed as a betrayal of young people.

She criticised Clegg, the deputy prime minister, for comparing the public finances with a household budget in his speech to the Liberal Democrat conference last week.

"Think about it, because this is a family with a choice to make," she said. "It's a family with a mortgage who cut the repayments when dad lost his job in the recession – to make sure they could get by until he found work, and to make sure the family didn't lose their home.

"And now they have a choice – make good those repayments steadily, bit by bit, go for some extra overtime or promotion, tighten their belts a little, but spread the payments sensibly.

"Or follow the George Osborne plan – pay it off all at once. Sell the furniture, the car that gets mum to work, sell the dog, even the house itself – whatever it takes to get the debt down. The truth is that every family knows cutting back too far, too fast, causes deep damage and ends up costing you far, far more."